$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 8x - 5$ and $ JT = 5x + 4$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {8x - 5} = {5x + 4}$ Solve for $x$ $ 3x = 9$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 8({3}) - 5$ $ JT = 5({3}) + 4$ $ CJ = 24 - 5$ $ JT = 15 + 4$ $ CJ = 19$ $ JT = 19$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {19} + {19}$ $ CT = 38$